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Is beauty truth, and truth beauty? The two are
intimately connected, possibly because our
minds react similarly to both. But what works
in mathematics need not work in physics, and
[5] vice versa. The relationship between
mathematics and physics is deep, subtle, and
puzzling. It is a philosophical conundrum of the
highest order – how science has uncovered
apparent “laws” in nature, and why nature
[10] seems to speak in the language of
mathematics.
Is the universe genuinely mathematical? Are its
apparent mathematical features mere human
inventions? Or does it seem mathematical to us
[15] because mathematics is the deepest aspect of
its infinitely complex nature that we are able to
understand?
Mathematics is not some disembodied version
of ultimate truth, as many used to think. If
[20] anything emerges from our tale, it is that
mathematics is created by people. ........
mathematicians are human and live ordinary
human lives, the creation of new mathematics
is partly a social process. But neither
[25] mathematics nor science is wholly the result of
social processes, as social relativists often
claim. Both must respect external constraints:
logic, in the case of mathematics, and
experiment, in the case of science. However
[30] desperately mathematicians might want to
trisect an ∠ by Euclidean methods, the
plain fact is that it is impossible. However
strongly physicists might want Newton's law of
gravity to be the ultimate description of the
[35] universe, the motion of the perihelion of
Mercury proves that it's not. This is why
mathematicians are so stubbornly logical, and
obsessed by concerns that most people could
not care less about. Does it really matter
[40] whether you can solve a quintic by radicals?
History's verdict on this question is
unequivocal. It does matter. It may not matter
directly for everyday life, but it surely matters
to humanity as a whole – not because anything
[45] important rests on being able to solve quintic
equations, but because understanding why we
can't opens a secret doorway to a new
mathematical world. If Galois and his
predecessors had not been obsessed with
[50] understanding the conditions under which an
equation can be solved by radicals, humanity's
discovery of group theory would have been
greatly delayed, and perhaps might not have
happened.
[55] You may not encounter groups in your kitchen
or on your drive to work, but without them
today's science would be severely curtailed,
and our lives would be far different. Not so
much in gadgetry like jumbo jets or GPS
[60] navigation or cell phones – though those are
part of the story too – but in insight into nature.
No one could have predicted that a pedantic
question about equations could reveal the deep
structure of the physical world, but that is what
[65] happened.
The clear message of history is a simple one.
Research on deep mathematical issues should
not be rejected or besmirched merely because
those issues seem to have no direct practical
[70] use. Good mathematics is more valuable than
gold, and where it comes from is mostly
irrelevant. What counts is where it leads.
Adapted from: STEWART, I. Why Beauty is Truth – The History of Symmetry. Cambridge, MA: Basic Books, 2007. p. 275-276.
Select the alternative that offers adequate synonyms to the words intimately (l. 02), genuinely (l. 12) and stubbornly (l. 37).
